Three of these expressions are equal to the volume of the house shown. Which expression is NOT?
g · h + (1/2 · j · k)
Volume of triangular prism + Volume of rectangular prism
g · h · [1/2(k – j) + j]
g · h · j + 1/2 · g · h · (k – j)
Three of these expressions are equal to the volume of the house shown. Which expression is NOT?
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To determine which expression is NOT equal to the volume of the house, we can analyze each formula based on the components involved in calculating the volume of a house composed of a rectangular prism and a triangular prism.
1. g · h + (1/2 · j · k): This expression suggests adding volumes, but it incorrectly adds an area (g · h) with a volume term (1/2 · j · k).
2. Volume of triangular prism + Volume of rectangular prism: This is a correct way to express the total volume of the house, assuming you are adding the two calculated volumes.
3. g · h · [1/2(k – j) + j]: This expression simplifies to the total volume based on the dimensions of both shapes involved, so it’s likely valid.
4. g · h · j + 1/2 · g · h · (k – j): This expression breaks down the volumes correctly based on the shapes involved.
Correct Answer: g · h + (1/2 · j · k) is NOT equal to the volume of the house.
Explanation: This expression inaccurately combines area and volume, leading to an incorrect total. The other expressions correctly combine dimensions to calculate the volume of both parts of the house. If you need any more detailed explanations, feel free to ask!